The two tests
Push the ring over the knuckle: it should take a small twist and a little resistance, not force. Then shake the hand downwards with the fingers open: the ring should stay put. If it passes the knuckle freely and stays put, it fits. If it will not pass, it is too small; if it slides off in the shake, too large. Those two tests cover almost every case, and every method on this site is only a way to reach a size that passes them.
Knuckles
On many hands the knuckle is wider than the base of the finger, sometimes by a full size. A ring sized to the base will not go on; a ring sized to the knuckle spins once past it. The usual compromise is a size between the two, which the measuring tool works out when you give it both lengths. For a big gap, jewellers can fit sizing beads or a sprung insert inside the band, which lets a smaller ring pass the knuckle.
Band width
A thin band touches the finger along a narrow line and can tilt to pass bone; a wide band touches a strip of skin and cannot. The same inner size therefore feels tighter as the band gets wider. The rule most jewellers use: up to 4 mm, the measured size; 6 mm, a quarter size up; 8 mm or more, a half size up. Comfort-fit bands, domed on the inside, touch less skin and go a quarter size the other way.
Weather, time and the body
Fingers are smallest first thing in the morning and in cold weather, largest in the evening, in heat, after exercise and after a salty meal or alcohol; the swing can be half a size. Weight changes, pregnancy, arthritis and age all move the size too, over months and years. Measure on a normal day in the late afternoon, more than once, and remeasure before buying anything expensive if the last measurement is more than a year old.
Between sizes
US quarter sizes are 0.64 mm of circumference apart, UK halves 0.625 mm, so most measurements land close to a stocked size. When yours does not, the converter shows the gap. Lean smaller for a thin band that can be resized, larger for a wide band, and larger for any ring that cannot be resized: eternity rings with stones all round, tension settings, and bands in tungsten, titanium or ceramic, which most jewellers will not cut.
Rings that cannot be resized
Resizing cuts the band and adds or removes metal, so it works on plain gold, silver and platinum and on rings with stones at the top only. It does not work on full eternity rings, most alternative metals, and rings with patterns or enamel round the band. For those, measure twice, use the larger of two close sizes, and buy from a seller who exchanges sizes.
Which finger and which hand
Size the finger the ring will live on, on that hand. The dominant hand runs about a quarter size larger, the index finger a size or two larger than the ring finger, the little finger two or three sizes smaller. A ring moved between fingers almost always needs resizing.